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**Anna University**

**Question Paper Code : 25059**

**B.E/B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2018.**

**Fifth**

**Semester**

**Computer Science and Engineering**

**MA 6566 Discrete Mathematics**

**( Regulation 2013 )**

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MA6566 DISCRETE MATHEMATICS

OBJECTIVES:

To extend student‟s Logical and Mathematical maturity and ability to deal with abstraction and to introduce most of the basic terminologies used in computer science courses and application of ideas to solve practical problems.

UNIT I LOGIC AND PROOFS 9+3

Propositional Logic – Propositional equivalences – Predicates and Quantifiers – Nested Quantifiers – Rules of inference – Introduction to proofs – Proof methods and strategy.

UNIT II COMBINATORICS 9+3

Mathematical induction – Strong induction and well ordering – The basics of counting – The pigeonhole principle – Permutations and combinations – Recurrence relations – Solving linear recurrence relations – Generating functions – Inclusion and exclusion principle and its applications.

UNIT III GRAPHS 9+3

Graphs and graph models – Graph terminology and special types of graphs – Matrix representation of graphs and graph isomorphism – Connectivity – Euler and Hamilton paths.

UNIT IV ALGEBRAIC STRUCTURES 9+3

Algebraic systems – Semi groups and monoids – Groups – Subgroups – Homomorphism‟s – Normal subgroup and cosets – Lagrange‟s theorem – Definitions and examples of Rings and Fields.

UNIT V LATTICES AND BOOLEAN ALGEBRA 9+3

Partial ordering – Posets – Lattices as posets – Properties of lattices – Lattices as algebraic systems – Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra.

TOTAL (L: 45+T:15): 60 PERIODS

OUTCOMES:

At the end of the course, students would:

Have knowledge of the concepts needed to test the logic of a program.

Have an understanding in identifying structures on many levels.

Be aware of a class of functions which transform a finite set into another finite set which relates to input and output functions in computer science.

Be aware of the counting principles.

Be exposed to concepts and properties of algebraic structures such as groups, rings and fields.

1. Kenneth H.Rosen, “Discrete Mathematics and its Applications”, 7th Edition, Tata Mc Graw Hill Pub. Co. Ltd., New Delhi, Special Indian Edition, 2011.2. Tremblay J.P. and Manohar R, “Discrete Mathematical Structures with Applications to Computer Science”, Tata Mc Graw Hill Pub. Co. Ltd, New Delhi, 30th Reprint, 2011.

1. Ralph.P.Grimaldi., “Discrete and Combinatorial Mathematics: An Applied Introduction”, 4th Edition, Pearson Education Asia, Delhi, 2007.2. Thomas Koshy., “Discrete Mathematics with Applications”, Elsevier Publications, 2006. 3.Seymour Lipschutz and Mark Lipson., “Discrete Mathematics”, Schaum‟s Outlines, Tata Mc Graw Hill Pub. Co. Ltd., New Delhi, 3rd Edition, 2010. 52

OBJECTIVES:

To extend student‟s Logical and Mathematical maturity and ability to deal with abstraction and to introduce most of the basic terminologies used in computer science courses and application of ideas to solve practical problems.

UNIT I LOGIC AND PROOFS 9+3

Propositional Logic – Propositional equivalences – Predicates and Quantifiers – Nested Quantifiers – Rules of inference – Introduction to proofs – Proof methods and strategy.

UNIT II COMBINATORICS 9+3

Mathematical induction – Strong induction and well ordering – The basics of counting – The pigeonhole principle – Permutations and combinations – Recurrence relations – Solving linear recurrence relations – Generating functions – Inclusion and exclusion principle and its applications.

UNIT III GRAPHS 9+3

Graphs and graph models – Graph terminology and special types of graphs – Matrix representation of graphs and graph isomorphism – Connectivity – Euler and Hamilton paths.

UNIT IV ALGEBRAIC STRUCTURES 9+3

Algebraic systems – Semi groups and monoids – Groups – Subgroups – Homomorphism‟s – Normal subgroup and cosets – Lagrange‟s theorem – Definitions and examples of Rings and Fields.

UNIT V LATTICES AND BOOLEAN ALGEBRA 9+3

Partial ordering – Posets – Lattices as posets – Properties of lattices – Lattices as algebraic systems – Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra.

TOTAL (L: 45+T:15): 60 PERIODS

OUTCOMES:

At the end of the course, students would:

Have knowledge of the concepts needed to test the logic of a program.

Have an understanding in identifying structures on many levels.

Be aware of a class of functions which transform a finite set into another finite set which relates to input and output functions in computer science.

Be aware of the counting principles.

Be exposed to concepts and properties of algebraic structures such as groups, rings and fields.

**TEXT BOOKS:**1. Kenneth H.Rosen, “Discrete Mathematics and its Applications”, 7th Edition, Tata Mc Graw Hill Pub. Co. Ltd., New Delhi, Special Indian Edition, 2011.2. Tremblay J.P. and Manohar R, “Discrete Mathematical Structures with Applications to Computer Science”, Tata Mc Graw Hill Pub. Co. Ltd, New Delhi, 30th Reprint, 2011.

**REFERENCES:**1. Ralph.P.Grimaldi., “Discrete and Combinatorial Mathematics: An Applied Introduction”, 4th Edition, Pearson Education Asia, Delhi, 2007.2. Thomas Koshy., “Discrete Mathematics with Applications”, Elsevier Publications, 2006. 3.Seymour Lipschutz and Mark Lipson., “Discrete Mathematics”, Schaum‟s Outlines, Tata Mc Graw Hill Pub. Co. Ltd., New Delhi, 3rd Edition, 2010. 52

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